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Analysis of asymptotic behavior in structurally damped evolution equations, highlighting decay rates.
In this paper, we are interested in analyzing the asymptotic profiles of solutions to the Cauchy problem for structurally damped ‐evolution equations in ‐sense. Depending on the parameters and we would like to not only indicate the approximation formula of solutions to both linear and nonlinear problems but also recognize the optimality of their decay rates in the distinct cases of parabolic like damping and ‐evolution like damping when the spatial dimension is sufficiently high. Moreover, some sharp blow‐up solution results for the low dimensional cases of the corresponding linear equation are also discussed in this work.
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Bui et al. (2026) studied this question.
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